Problem of Negation, Paradox of NON-Existence, Theorem of Existence

The question of the Theorem of Existence is very simple. That theorem theorem follows immediately from the definition of the TOTAL Universe :

The TOTAL Universe is by definition the Set of all things. Therefore, all things exist in that set and the opposite of all things too.

Any other definition or conception of the Universe, which is not equivalent to that one, leads to a very vicious paradox. That paradox is hidden in the current idea according to which "Certain things do not exist". When expressed very rigorously with the existential quantifier, that sentence says this : "THERE ARE things that ARE NOT", or "THER EXISTE things that do not EXIST".

The contrary of that sent needs the universal quantifier to be expressed. That contrary is simply this : "ALL things exist". This is the Theorem of Existence, which is very closely associated with the concept of TOTAL Universe.